Quantum Monte Carlo algorithm

In the second part we have given a short introduction and review of modern world line quantum Monte Carlo algorithms for quantum systems, which are free of any time discretization errors. We have highlighted the fact that... 

C. Lin, F. H. Zong, and D. M. Ceperley (2001) Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms. Phys. Rev. E 64, 016702(1-12]... 

The Original Reptation Quantum Monte Carlo Algorithm... 

A. Aspuru-Guzik et al., A sparse algorithm for the evaluation of the local energy in quantum Monte Carlo. J. Comp. Chem. 26, 708-715 (2005)... 

Quantum Monte Carlo World Line Algorithms.613... 

The Diffusion Quantum Monte Carlo (DQMC) algorithm and related methods such as the Vibrational Quantum Monte Carlo approach have the important property of scahng well with system size (number of degrees of freedom). At the same time the method can be pursued in principle to yield a numerically exact energy. DQMC was introduced... 

The material presented above was selected to describe from a unified point of view Monte Carlo algorithms as employed in seemingly unrelated areas in quantum and statistical mechanics. Details of applications were given only to explain general ideas or important technical problems, such as encountered in diffusion Monte Carlo. We ignored a whole body of literature, but we wish to just mention a few topics. Domain Green function Monte Carlo [25-28] is one that comes very close to topics that were... 

Increases in computer power and improvements in algorithms have greatly extended the range of applicability of classical molecular simulation methods. In addition, the recent development of Internal Coordinate Quantum Monte Carlo (ICQMC) has allowed the direct comparison of classical simulations and quantum mechanical results for some systems. In particular, it has provided new insights into the zero point energy problem in many body systems. Classical studies of non-linear dynamics and chaos will be compared to ICQMC results for several systems of interest to nanotechnology applications. The ramifications of these studies for nanotechnology applications will be discussed. 

Because many details of the dynamics and structure of chemical systems cannot be directly observed, molecular simulation methods such as molecular dynamics (MD) [1-31, molecular mechanics (MM) [4], and classical and quantum Monte Carlo [5,6] are extremely valuable tools for making sense of experimental results. In the context of nanotechnology, molecular simulation is crucial for studying the feasibility of proposed directions of research and development [7], With the rapid improvement in computing power and algorithms, the capabilities and range of applicability of molecular simulation have dramatically increased over the past decade. 

Alternative strategies have also been proposed for estimating correlation energies, including quantum Monte Carlo methods (see reference 67 and references therein), MP2 schemes, either canonical " " or based on the Laplace transform algorithm, and the molecular-like incremental method applied by Stoll.However, none of these methods seems to have arrived at a sufficiently advanced stage of development to be of general use to the scientist at the moment. 

Fisher DR et al (2008) An optimized initialization algorithm to ensure accuracy in quantum Monte Carlo calculatitnis. J Comput Chem 29(14) 2335-2343... 

The variational quantum Monte Carlo method (VMC) is both simpler and more efficient than the DMC method, but also usually less accurate. In this method the Rayleigh-Ritz quotient for a trial function 0 is evaluated with Monte Carlo integration. The Metropolis-Hastings algorithm " is used to sample the distribution... 

The general idea of the world-line Monte Carlo algorithm is similar to that of the quantum-to-classical mapping discussed in the last section. The Hamiltonian is split into two or more terms H = ft such that the matrix... 

To provide quantitative predictions about how to detect the superfluid-insulator transition in these experiments, Kashurnikov, Prokofev and Svistunov performed quantum Monte Carlo simulations of the singleparticle density matrix p,y = (I I /). They used the Bose-Hubbard model with harmonic confining potential and carried out world-line Monte Carlo simulations with the continuous-time Worm algorithm. The diagonal elements of the density matrix provide the real-space particle density, and... 

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